In air transportation, the problem of boarding quickly affects both airlines and passengers alike. New research by Jason Steffen, a physicist at the Fermilab in Batavia, Illinois, gives some insight into how the boarding procedure could be improved. Steffen applied a computational technique known as the Monte Carlo algorithm to simulate the boarding of an aircraft. The simulation admitted passengers on board at random, each with a predetermined seat number, and each taking a random amount of time stowing their luggage (which he assumes is the biggest cause of delay). Then Steffen looked for the boarding patterns that filled the aircraft the quickest. The worst method, unsurprisingly, was boarding front-to-back, but the usual method (back-to-front) was only slightly better. The quickest patterns all indicated that there should be more attention placed on the relative positions of the seats. Two methods he suggested included boarding groups of people in rows that were widely separated from each other and boarding window seats first. Steffen showed that these strategies could halve the boarding time and are so efficient that they would work better than the usual methods even if some people didn't board in the right order.

In this article, Bryan Nelson reports on some work in the field of computer vision that may eventually be used to detect forgeries. Using the works of five of the world's greatest painters (Rembrandt, van Gogh, Dali, Magritte, and Kandinsky), computer science professor Daniel Keren at the University of Haifa has developed a computer program that has been fairly successful at correctly distinguishing the style, and paintings, of one artist from another. The program works by dividing each painting into small, discrete blocks, then computing certain values for each block, based upon certain features the program has been taught to identify. Based upon these values, each block can be mapped to a specific artist, although the overall painting can be classified as well. Read more about Keren's work online.

In 1962 Massachusetts Institute of Technology mathematician Edward Thorp published Beat the Dealer, a book about how to win at blackjack. One might expect that Thorp's method of card counting described in the book would make him unwelcome at Las Vegas casinos, but instead he is very popular in Las Vegas and gave the keynote address to an overflow crowd at the recent World Game Protection Conference. It turns out that Thorp's book, which is still in print and has sold over a half-million copies, helped increase the popularity of blackjack because people feel that they can use strategies to win. The book also led to changes in blackjack, including the use of multiple decks. Said one casino security consultant about Thorp's address, "This is like going back in time and seeing Babe Ruth to me. Here's the man who started it all."

Mathematician Andrew Wiles received worldwide fame in 1995 for solving Fermat's Last Theorem, first posed 350 years earlier, but few know that Sophie Germain---a French woman who disguised her gender and worked with such famous mathematicians as Gauss, Legendre, and Lagrange---made a solid attempt to solve the problem as well. Germain was the first woman to do significant research in mathematics, and her attack on Fermat's theorem was recently uncovered by two American professors who combed through her notes that were stored in a French library. Her approach to Fermat's last theorem is significant because she was one of the first to propose a method for proving the theorem for all numbers, not just individual cases. Her accomplishment is even more remarkable because she did not have a formal mathematical education. She did take the name of a male student in order to correspond with professors at the university, but her notes reveal that she probably worked alone.

"Maths in action": Review of How Round is Your Circle?, by John Bryant and Chris Sangwin. Reviewed by Mattew Killeya. New Scientist, 23 February 2008, page 50.

This short review calls this "a gem of a book" that reveals why mathematics is crucial to engineering and understanding the world. "[T]he authors do a refreshing job of bringing out the mathematics you learned in school but sadly never knew why," the reviewer writes.

"Looking behind the numbers": Interview with John Ioannidis. Interviewed by Jim Giles. New Scientist, 16 February 2008, page 45.

In 2005, clinical epidemiologist John Ioannidis published in a prominent medical journal a paper called ``Why most published research findings are false''. Ioannidis trained in internal medicine, but he also liked mathematics and found it difficult to choose between the two. In addition to a medical degree, he earned a PhD in biopathology and nowadays holds faculty positions at the University of Ioannina in Greece and Tufts University in Boston. After coming into contact with researchers who were doing meta-analysis of medical studies, Ioannidis became interested in, as he puts it in the interview, ``how to inject robust quantitative thinking into clinical work''. His work uses sophisticated statistical techniques to analyze medical studies. In his 2005 paper, he used these techniques to try to model the probability of a research finding being true. ``For some areas, if you get a positive result then it is 85 percent or even 90 percent likely to be true,'' Ioannidis told the interviewer. ``That is the case for very large-scale randomized clinical trials with very clear protocols, full reporting of results and a long chain of research supporting the finding beforehand. Then there is the other extreme, where an experiment is so poorly designed or so many analyses are performed that a statistically significant finding wouldn't have better than a 1-in-1000 chance of being true.''

Three articles appeared together as a brief report on sessions related to new advances in Number Theory at the Joint Mathematics Meetings of 2008, held in San Diego.

"A Woman Who Counted": The work of Sophia Germain, a mathematician who lived in the 19th century, has never been fully appreciated until now. What little knowledge we had of her mathematics came from a footnote in the work of Legendre, who refers to her work in his proof of Fermat's Last Theorem for n=5. Recently, two mathematicians from New Mexico State University and Virginia Polytechnic Institute began reading manuscripts and letters in which Germain laid out a plan for proving the theorem in generality. Her unique approach to the problem establishes Germain as Legendre's contemporary rather than simply his protégé. Although much of her novel plan was rediscovered later and did not lead to a proof, this shows her true accomplishments merit much more than a footnote.

"Number Theorists' Big Cover-Up Proves Harder Than It Looks": Fermat's Last Theorem isn't the only "easy to state, hard to prove" theorem in number theory, one of the oldest branches of mathematics. This article gives two examples of conjectures made over 30 years ago that are still being explored today. One of Paul Erdös's "favorite problems" concerned the covering of the integers by arithmetic sequences. He conjectured that there is a finite collection of arithmetic sequences that cover the integers and whose smallest step size is as large as one wants. This conjecture remains unproven, and 1040 sequences are needed to cover the integers when the smallest step size is 36---that's more than the number of stars in the observable universe. Although not directly connected to Erdös's conjecture, the identification of large prime numbers, which is key in protecting our privacy on the internet, is furthered by covering theory. Extending the work of Sierpinski, Selfridge conjectured that each sequence in a family of almost 80,000 sequences contains at least one prime. Online collaboration allowed many computers to tackle the huge computations necessary to confirm his conjecture for all but six such progressions that have yet to be evaluated.

"Exact-Postage Poser Still Not Licked": The Diophantine Problem of Frobenius was posed over 100 years ago and is another example of an unsolved yet well-studied problem in number theory. One version of this problem is to find the largest amount of postage not payable using two stamps of different values. For just two values, there is a simple formula determining this largest impossible postage. For three or more different values of stamps, there is no such formula. Recent advances using computational algebraic geometry now solve the problem via computer for combinations of up to 13 digits long with values up to ten digits long. But the problem is NP-hard, so a practical solution able to handle larger numbers might only be found in the distant future.

"Baseball's Devil May Not Be in the Details," by Alan Schwarz. New York Times, 10 February 2008.

Following the recent steroid scandal in major league baseball, Congressman Mark Souder (R-IN) proposed that players with suddenly improving statistics be tested more frequently for performance-enhancing drugs. But can you really judge steroid use by looking at batting average? Attempts to compare various measures—home run totals, on-base time, etc.—between those who were and were not accused of steroid use has shown only minor differences, and some players even performed worse after starting the drugs. Most experts agree that steroid use will have some effect on a player's numbers, but there are many other possible explanations for the fluctuations and many examples of steroid-free players—such as Hank Aaron, who hit home runs more frequently in his late 30s—who would have been caught in the net of improbably high statistics. The problem with placing so much emphasis on these numbers, claim experts quoted in the article, is that too many factors influence these statistics for them to be a reliable indicator of any one thing.

Avraham Trakhtman, a professor at Bar-Ilan University (Israel), has solved the Road Coloring Problem, first posed in 1970. One statement of the problem is that given a map of N cities and 2N one-way roads, for which each city has exactly two roads leading out of it, and at least one leading in, is it possible to color each road red or blue, so that "universal directions" can be given? Universal directions are those that will get a traveler to his or her destination regardless of his or her location on the map (a more precise statement is online). One such map-coloring, from Wikipedia, is at left. Trakhtman has answered the question in the affirmative. His solution will be published in the Israel Journal of Mathematics. An abstract is online. Trakhtman immigrated to Israel from the Soviet Union in 1990. He worked as a guard for five years before becoming a professor at Bar-Ilan.

"How Much is a Trillion?" by Ira Flatow. Science Friday, National Public Radio, 8 February 2008.

On the Friday following President Bush's unveiling of his US$3.1 trillion budget, Science Friday host Ira Flatow interviewed writer and storyteller David M. Schwartz on the subject of very large numbers. Schwartz, author of a number of children's books, including How Much is a Million?, If You Made a Million, and Millions To Measure, discussed how he conveys the concept of very large numbers to children and teachers. Essentially, he does this by taking relatively small quantities of familiar units or objects and comparing them with larger amounts of the same unit or object. For example, Schwartz notes that one million seconds equals about 11.5 days. Now compare this to one billion seconds: this equals roughly 32 years, while one trillion seconds equals almost 32,000 years! Or, given that a stack of 100 dollar-bills is about half an inch high, he finds the height of US$1 million dollars in dollar-bills, then US$1 billion, US$1 trillion, and finally US$3.1 trillion in dollar-bills, and compares this to the height of Mount Everest. He also finds out how many Mount Everests you'd have to stack to equal the height of US$3.1 trillion dollars.

Patrick Ball helped build the case against former dictator Slobodan Milosevic for an international criminal tribunal not by examining laws Milosevic violated, but by carefully comparing migration patterns to the ups and downs of the ongoing war. His conclusion? Bombings and violence by both sides were not the cause of migration surges—but a specific effort to remove people from their homes could have been. Ball, a statistician, has spent his career collecting and analyzing data on migration and death tolls from Yugoslavia to Peru in an effort to help sort out the truth of human rights violations. He realizes, however, that statistics alone provides only a measure of plausibility, a way to rule things out. The numbers cannot supply the correct alternative explanation, and a graph cannot demonstrate how it felt to experience the atrocity.

With the help of SUNY mathematics professor David Hobby, AMS Public Awareness Officer Mike Breen, and some U.S. Department of Labor Bureau of Labor Statistics data, this article provides the general reader with some answers to the question: What do mathematicians do? They may do mathematical research, as does Hobby, "the goal [being] to figure out general rules and then prove that they work." They may be mathematics teachers or professors. They may be actuaries, cryptanalysts, statisticians, engineers, computer scientists, or operations researchers who apply mathematics to solve "real-world" problems. They may work for the government, or in industry or academia. What mathematicians have in common is their ability to solve problems, pay attention to details, and be highly creative, according to Breen.

"Microsoft Adds Research Lab in East as Others Cut Back," by Katie Hafner. The New York Times, 4 February 2008.

Microsoft announced recently that in July 2008 it will be opening a sixth research lab, this one in Cambridge, next door to the Massachusetts Institute of Technology. The lab would focus on pure research, rather than product development, and will be led by Jennifer Tour Chayes, a mathematical physicist. "We believe that in the long run, putting money into basic research will pay off, but you have to wait longer for it," says Chayes. The veteran researcher explains that later on the "development people" will use the insights gathered from the research to create new products. The labs also offer a high level of intellectual freedom, which Chayes cites as one of the main reasons she stays content at Microsoft. Microsoft Research, which houses about 800 researchers with doctorates, is becoming one of the few corporate research labs that is growing in size rather than shrinking, with perhaps Google labs being the only exception. It is also one of the first labs of this nature to have a female director. As such, Chayes hopes to also become a role model for women in mathematics and the computer sciences.

Begley tests different voting methods offered by the American Statistical Association, and reports how voting methods determine the outcomes. She notes, "For anyone who believes in democracy, this is a little disturbing. What it means is that `election outcomes can more accurately reflect the choice of an election rule than the voters' wishes,' writes mathematician Donald Saari of the University of California, Irvine." Anyone may try the three voting methods to choose among four candidates from the Democratic and from the Republican party in this year's Presidential elections and see the results on an interactive voting methods on the website, one of the 2008 Mathematics Awareness Month "Mathematics and Voting" theme resources at www.amstat.org/mathandvoting.

"No god required": Review of Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up, by John Allen Paulos. Reviewed by Amanda Gefter. New Scientist, 2 February 2008, page 48.

In his latest book, Paulos "wades through the classical arguments for the existence of God and systematically refutes them," the reviewer writes. She enjoyed the book but was hoping for a new, more specifically mathematical perspective. What she found, though, is that the book "covers well-trodden ground".

Ronald Fedkiw, a computer scientist at Stanford University who has a Ph.D. in applied mathematics from the University of California, Los Angeles, recently received an Academy Award for his work improving Hollywood special effects. The raging seas in Pirates of the Caribbean and other fluid simulations in movies rely on a method Fedkiw created in the early 2000s, originally as a tool for computational physics. Fedkiw says that the method's application to film "was just luck."